Cosmological perfect fluids in higher-order gravity

We prove that in Robertson–Walker space-times (and in generalized Robertson–Walker spacetimes of dimension greater than 3 with divergence-free Weyl tensor) all higher-order gravitational corrections of the Hilbert–Einstein Lagrangian density F(R, □ R, … , □ kR) have the form of perfect fluids in the field equations. This statement definitively allows to deal with dark energy fluids as curvature effects.